Phase Transitions and Gravitational Waves

TL;DR

This paper forecasts the detectability of gravitational waves from early universe phase transitions using Fisher analysis for DECIGO and LISA, focusing on key parameters like transition strength and duration.

Contribution

It introduces a Fisher-matrix approach to estimate how well future detectors can measure parameters of gravitational wave signals from phase transitions.

Findings

Fisher analysis yields ~0.12 uncertainty in log(α) for the parameters.

Uncertainties in log(β/H*) are around 0.145, showing precise parameter estimation.

Strong correlation (~0.98) between the parameters α and β/H*.

Abstract

We present a Fisher-matrix forecast for the detectability of a stochastic gravitational wave background generated by a first-order phase transition in the early universe. We use the DECIGO and LISA missions as reference cases. The source gravitational wave spectrum $\Omega_{\rm GW}(f)$ is modeled as the sum of sound wave and turbulence contributions and is parameterized by the transition strength $\alpha$, its inverse duration $\beta/H_*$, its transition temperature $T_{*}$, and the bubble wall velocity $v_{w}$. For each detector, we construct fiducial models with signal peaking in the sensitivity band of the detector, fixing $T_{*}$ and $v_{w}$, and perform a Fisher analysis on the remaining parameters $\ln\alpha$ and $\ln(\beta/H_{*})$. A two-parameter Fisher analysis in $\{\ln\alpha,\ln(\beta/H_{*})\}$, with fixed values of $T_{*}$ and $v_{w}$, yields marginalized $1\sigma $ uncertainties $\sigma(\ln\alpha)\simeq 0.12$ and $\sigma[\ln(\beta/H_{*})]\simeq 0.145$. The parameters are strongly correlated, with correlation coefficient $\mathrm{corr}\simeq 0.98$. We perform a corresponding analysis for LISA and report marginalized $1\sigma$ uncertainties $\Delta\alpha/\alpha \simeq {}^{+0.044}_{-0.042}$ and $\Delta(\beta/H_{*})/(\beta/H_{*}) \simeq {}^{+0.119}_{-0.107}$, with correlation coefficient $\mathrm{corr}\simeq 0.78$.